{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": "/9j/4AAQSkZJRgABAQEBLAEsAAD/7S4GUGhvdG9zaG9wIDMuMAA4QklNBCUAAAAAABAAAAAAAAAA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\nphy+Op7fwL/jxx5Kfzf+uLH2p/xfT/HH/9k=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image \n",
    "Image('https://github.com/unpingco/Python-for-Probability-Statistics-and-Machine-Learning/raw/master/python_for_probability_statistics_and_machine_learning.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from matplotlib.pylab import subplots\n",
    "import numpy as np\n",
    "from sklearn.datasets import make_blobs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clustering is the simplest member of a family of machine learning methods that\n",
    "do not require supervision to learn from data. Unsupervised methods\n",
    "have training sets that do not have a target variable. These unsupervised\n",
    "learning\n",
    "methods rely upon a meaningful metric to group data into\n",
    "clusters. This makes it an excellent exploratory data analysis\n",
    "method because there are very few assumptions built into the method itself.\n",
    "In this section, we focus on the popular K-means clustering method that is\n",
    "available in Scikit-learn.\n",
    "\n",
    "Let's manufacture some data to get going with `make_blobs` from Scikit-learn.\n",
    "[Figure](#fig:clustering_001) shows some example clusters in two dimensions.\n",
    "Clustering methods work by minimizing the following objective function,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "2"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASMAAAEACAYAAAD4GBC1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGGOKwMGIMaYI/w+mRTja1lrpUgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb11d2f290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "fig,ax=subplots()\n",
    "X, y = make_blobs(n_samples=300, centers=4,\n",
    "                  random_state=0, cluster_std=1.0)\n",
    "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray');\n",
    "ax.tick_params(labelsize='x-large')\n",
    "ax.set_aspect(1/1.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/clustering_001.png, width=500 frac=0.85]\n",
    "The four clusters are pretty easy to see in this example and we want clustering\n",
    "methods to determine the extent and number of such clusters automatically.  <div\n",
    "id=\"fig:clustering_001\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:clustering_001\"></div>\n",
    "\n",
    "<p>The four clusters are pretty easy to see in this example and we want\n",
    "clustering methods to determine the extent and number of such clusters\n",
    "automatically.</p>\n",
    "<img src=\"fig-machine_learning/clustering_001.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "$$\n",
    "J = \\sum_k \\sum_i \\Vert \\mathbf{x}_i-\\mathbf{\\mu}_k \\Vert^2\n",
    "$$\n",
    "\n",
    " The *distortion* for the $k^{th}$ cluster is the summand,\n",
    "\n",
    "$$\n",
    "\\Vert x_i - \\mathbf{ \\mu }_k \\Vert^2\n",
    "$$\n",
    "\n",
    " Thus, clustering algorithms work to minimize this by adjusting the\n",
    "centers of the individual clusters, $\\mu_k$. Intuitively, each $\\mu_k$ is the\n",
    "*center of mass* of the points in the cloud.  The Euclidean distance is\n",
    "the typical metric used for this,\n",
    "\n",
    "$$\n",
    "\\Vert \\mathbf{ x } \\Vert^2 = \\sum x_i^2\n",
    "$$\n",
    "\n",
    " There are many clever algorithms that can solve this problem for\n",
    "the best $\\mu_k$ cluster-centers. The K-means algorithm starts with a\n",
    "user-specified number of $K$ clusters to optimize over.  This is implemented in\n",
    "Scikit-learn with the `KMeans` object that follows the usual fitting\n",
    "conventions in Scikit-learn,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "    n_clusters=4, n_init=10, n_jobs=1, precompute_distances='auto',\n",
       "    random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(n_clusters=4)\n",
    "kmeans.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where we  have chosen $K=4$. How do we choose the value of\n",
    "$K$?  This is the eternal question of generalization versus\n",
    "approximation --- too many clusters provide great approximation but\n",
    "bad generalization. One way to approach this problem is to compute the\n",
    "mean distortion for increasingly larger values of $K$ until it no\n",
    "longer makes sense. To do this, we want to take every data point and\n",
    "compare it to the centers of all the clusters.  Then, take the\n",
    "smallest value of this across all clusters and average those. This\n",
    "gives us an idea of the overall mean performance for the $K$ clusters.\n",
    "The following code computes this explicitly.\n",
    "\n",
    "**Programming Tip.**\n",
    "\n",
    "The `cdist` function from Scipy computes all the pairwise\n",
    "differences between the two input collections according to the\n",
    "specified metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "4"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import cdist\n",
    "m_distortions=[]\n",
    "for k in range(1,7):\n",
    "    kmeans = KMeans(n_clusters=k)\n",
    "    _=kmeans.fit(X)\n",
    "    tmp=cdist(X,kmeans.cluster_centers_,'euclidean')\n",
    "    m_distortions.append(sum(np.min(tmp,axis=1))/X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "5"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgoAAAFJCAYAAAD65QUKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npKAgIiIiVfp/ud2yQv9D2xUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb0b835510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=subplots()\n",
    "fig.set_size_inches((8,5))\n",
    "_=ax.plot(m_distortions,'-o',ms=10,color='gray')\n",
    "_=ax.set_xlabel('K',fontsize=16)\n",
    "_=ax.set_ylabel('Mean Distortion',fontsize=16)\n",
    "ax.tick_params(labelsize='x-large')\n",
    "# ax.set_aspect(1/1.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/clustering_002.png, width=500 frac=0.75]\n",
    "The Mean Distortion shows that there is a diminishing value in using more\n",
    "clusters.  <div id=\"fig:clustering_002\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:clustering_002\"></div>\n",
    "\n",
    "<p>The Mean Distortion shows that there is a diminishing value in using more\n",
    "clusters.</p>\n",
    "<img src=\"fig-machine_learning/clustering_002.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    " Note that code above uses the `cluster_centers_`, which are\n",
    "estimated from K-means algorithm. The resulting [Figure](#fig:clustering_002)\n",
    "shows the point of diminishing returns for\n",
    "added additional clusters.\n",
    "\n",
    "\n",
    "Another figure-of-merit is the silhouette coefficient, which measures\n",
    "how compact and separated the individual clusters are. To  compute the\n",
    "silhouette coefficient, we need to compute the mean intra-cluster\n",
    "distance for each sample ($a_i$) and the mean distance to the next\n",
    "nearest cluster ($b_i$). Then, the silhouette coefficient for the\n",
    "$i^{th}$ sample is\n",
    "\n",
    "$$\n",
    "\\texttt{sc}_i = \\frac{b_i-a_i}{\\max(a_i,b_i)}\n",
    "$$\n",
    "\n",
    " The mean silhouette coefficient is just the mean of all these values\n",
    "over all the samples.  The best value is one and the worst is negative one,\n",
    "with values near zero indicating overlapping clusters and negative values\n",
    "showing that samples have been incorrectly assigned to the wrong cluster.  This\n",
    "figure-of-merit is implemented in Scikit-learn as in the following,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "6"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "7"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEICAYAAABLdt/UAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb0ad86dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def scatter_fit(X,y,ax):\n",
    "    _=kmeans.fit(X)\n",
    "    _=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='.')\n",
    "    _=ax.set_title('silhouette={:.3f}'.format(silhouette_score(X,kmeans.labels_)))\n",
    "\n",
    "fig,axs = subplots(2,2,sharex=True,sharey=True)\n",
    "np.random.seed(12)\n",
    "ax=axs[0,0]\n",
    "X,y=make_blobs(centers=[[0,0],[3,0]],n_samples=100)\n",
    "scatter_fit(X,y,ax)\n",
    "ax=axs[0,1]\n",
    "X,y=make_blobs(centers=[[0,0],[10,0]],n_samples=100)\n",
    "scatter_fit(X,y,ax)\n",
    "ax=axs[1,0]\n",
    "X,y=make_blobs(centers=[[0,0],[3,0]],n_samples=100,cluster_std=[.5,.5])\n",
    "scatter_fit(X,y,ax)\n",
    "ax=axs[1,1]\n",
    "X,y=make_blobs(centers=[[0,0],[10,0]],n_samples=100,cluster_std=[.5,.5])\n",
    "scatter_fit(X,y,ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Figure](#fig:clustering_004) shows how the silhouette coefficient\n",
    "varies\n",
    "as the clusters become more dispersed and/or closer together.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/clustering_003.png, width=500 frac=0.85]\n",
    "The shows how the silhouette coefficient varies as the clusters move closer and\n",
    "become more compact. <div id=\"fig:clustering_003\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:clustering_003\"></div>\n",
    "\n",
    "<p>The shows how the silhouette coefficient varies as the clusters move closer\n",
    "and become more compact.</p>\n",
    "<img src=\"fig-machine_learning/clustering_003.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "K-means is easy to understand  and to implement, but can be sensitive\n",
    "to the initial choice of cluster-centers. The default initialization\n",
    "method in Scikit-learn uses a very effective and clever randomization\n",
    "to come up with the initial cluster-centers. Nonetheless, to see why\n",
    "initialization can cause instability with K-means, consider the\n",
    "following [Figure](#fig:clustering_004), In [Figure](#fig:clustering_004), there\n",
    "are two large clusters on the left and\n",
    "a very sparse cluster on the far right. The large circles at the\n",
    "centers are the cluster-centers that K-means found. Given $K=2$, how\n",
    "should the cluster-centers be chosen? Intuitively, the first two\n",
    "clusters should have their own cluster-center somewhere between them\n",
    "and the sparse cluster on the right should have its own cluster-center\n",
    "[^kmeans].\n",
    "Why isn't this happening?\n",
    "\n",
    "[^kmeans]: Note that we are using the `init=random` keyword argument for this\n",
    "example in order to illustrate this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "8"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmFyvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb0aec3b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,y = make_blobs(centers=[[0,0],[5,0]],random_state=100,n_samples=200)\n",
    "Xx,yx=make_blobs(centers=[[20,0]],random_state=100,n_samples=3)\n",
    "X=np.vstack([X,Xx])\n",
    "y=np.hstack([y,yx+2])\n",
    "\n",
    "fig,axs=subplots(2,1,sharex=True,sharey=True)\n",
    "ax=axs[0]\n",
    "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='.',alpha=.3);\n",
    "_=kmeans = KMeans(n_clusters=2,random_state=123,init='random')\n",
    "_=kmeans.fit(X)\n",
    "_=ax.set_aspect(1)\n",
    "_=ax.plot(kmeans.cluster_centers_[:,0],kmeans.cluster_centers_[:,1],'o',color='gray',ms=15,alpha=.5)\n",
    "\n",
    "X,y = make_blobs(centers=[[0,0],[5,0]],random_state=100,n_samples=200)\n",
    "Xx,yx=make_blobs(centers=[[20,0]],random_state=100,n_samples=10)\n",
    "X=np.vstack([X,Xx])\n",
    "y=np.hstack([y,yx+2])\n",
    "\n",
    "ax=axs[1]\n",
    "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='.',alpha=.3);\n",
    "kmeans = KMeans(n_clusters=2,random_state=123,init='random')\n",
    "_=kmeans.fit(X)\n",
    "_=ax.set_aspect(1)\n",
    "_=ax.plot(kmeans.cluster_centers_[:,0],kmeans.cluster_centers_[:,1],'o',color='gray',ms=15,alpha=.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/clustering_004.png, width=500 frac=0.85]\n",
    "The large circles indicate the cluster-centers found by the K-means algorithm.\n",
    "<div id=\"fig:clustering_004\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:clustering_004\"></div>\n",
    "\n",
    "<p>The large circles indicate the cluster-centers found by the K-means\n",
    "algorithm.</p>\n",
    "<img src=\"fig-machine_learning/clustering_004.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "The problem is that the objective function for K-means is trading the distance\n",
    "of the far-off sparse cluster with its small size. If we keep increasing the\n",
    "number of samples in the sparse cluster on the right, then K-means will move\n",
    "the cluster centers out to meet them,  as shown in\n",
    "[Figure](#fig:clustering_004). That is, if one of the initial cluster-centers\n",
    "was\n",
    "right in the middle of the sparse cluster, the the algorithm would have\n",
    "immediately captured it and then moved the next cluster-center to the middle of\n",
    "the other two clusters (bottom panel of [Figure](#fig:clustering_004)).\n",
    "Without some thoughtful initialization, this may not happen and the sparse\n",
    "cluster would have been merged into the middle cluster (top panel of\n",
    "[Figure](#fig:clustering_004)). Furthermore, such problems are hard to visualize\n",
    "with\n",
    "high-dimensional clusters. Nonetheless, K-means is generally very fast,\n",
    "easy-to-interpret, and easy to understand. It is straightforward to parallelize\n",
    "using the `n_jobs` keyword argument so that many initial cluster-centers can be\n",
    "easily evaluated.  Many extensions of K-means use different metrics beyond\n",
    "Euclidean  and incorporate adaptive weighting of features. This enables the\n",
    "clusters to have ellipsoidal instead of spherical shapes."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
